Here's one possible reason.
In conventional random tensor networks, even those with degrees of freedom on each of the links as in [1]}, the area operators associated to two crossing cuts commute.
That is, if you consider one cut through the tensor network, and then a second cut that crosses it (but nowhere overlaps it), the `areas' associated to those cuts can be simultaneously fixed.
This cannot happen for overlapping cuts in AdS/CFT [2]}.
There, crossing areas do not commute because the area is conjugate to the boost angle across the surface, and fixing one area makes the geometry of the Cauchy surface highly uncertain.
Hence simply adding link degrees of freedom does not capture this subtle behavior seen in gravity.
